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Applied Mathematics and Mechanics (English Edition) ›› 2011, Vol. 32 ›› Issue (9): 1187-1196.doi: https://doi.org/10.1007/s10483-011-1492-9

• Articles • 上一篇    下一篇

Uniformly ultimate boundedness for discontinuous systems with time-delay

慕小武1 丁志帅1 程桂芳1,2   

  1. 1. Department of Mathematics, Zhengzhou University, Zhengzhou 450001, P. R. China;
    2. Physical Engineering College, Zhengzhou University, Zhengzhou 450001, P. R. China
  • 收稿日期:2011-04-13 修回日期:2011-06-16 出版日期:2011-09-02 发布日期:2011-09-02

Uniformly ultimate boundedness for discontinuous systems with time-delay

 MU Xiao-Wu1, DING Zhi-Shuai1, CHENG Gui-Fang1,2   

  1. 1. Department of Mathematics, Zhengzhou University, Zhengzhou 450001, P. R. China;
    2. Physical Engineering College, Zhengzhou University, Zhengzhou 450001, P. R. China
  • Received:2011-04-13 Revised:2011-06-16 Online:2011-09-02 Published:2011-09-02

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摘要： The uniformly ultimate boundedness of discontinuous systems with time-delay in the sense of Filippov solutions is discussed. Based on the Lyapunov-Krasovskii functional, the Lyapunov theorem for the globally strongly uniformly ultimate boundedness of retarded discontinuous systems is presented. Furthermore, the result is applied to a class of mechanical systems with a retarded discontinuous friction item.

Abstract: The uniformly ultimate boundedness of discontinuous systems with time-delay in the sense of Filippov solutions is discussed. Based on the Lyapunov-Krasovskii functional, the Lyapunov theorem for the globally strongly uniformly ultimate boundedness of retarded discontinuous systems is presented. Furthermore, the result is applied to a class of mechanical systems with a retarded discontinuous friction item.

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